There is MySQL 5.1 on the default repository, but I'd like 5.6 for full-text search of InnoDB databases, and the new(er) SHA2 algorithms.

Edit
Also, I wanted to note that I have rebuilt the VM a few times (eliminate the issue of having a corrupt download), and Googled the issue. None of the results I've found have been helpful at all. Most of them were actually unanswered questions similarly to mine.

I never found a fix for my problem; I did get a solution. One of my issues was that I never had enough memory. A VM on my local machine was using 300MB or so, which was more than my VPS had. I tried a swap file, but my VPS runs on an OpenVZ kernel and they don't support swap files.

The solution ended up being a KVM VPS. It ended up costing a few bucks more a month with double the memory, storage, and bandwidth. MySQL 5.6 on Centos 6.5 runs just fine now.

Reading your log (messages), it shows a memory problem: mysqld is consuming all the available memory, and the OOM process kills it before it manages the whole system to hang...
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AndrewQDec 10 '13 at 15:53